Page 113 - Entrophy Analysis in Thermal Engineering Systems

106 Entropy Analysis in Thermal Engineering Systems

where Λ is a stochiometric coefficient. The number of moles of air supplied
to combust one mole of fuel is 4.76Λ. The minimum value of Λ corresponds
to stoichiometric combustion: Λ min ¼ x + . Also, n v denotes the num-
y
z
4 2
ber of moles of water vapor in the gaseous products, which depends on its
partial pressure [1].
ð
p sat T 0 Þ
n v
¼ (8.7)
p 0
n p
where p sat (T 0 ) is the saturation pressure of water at ambient temperature, and
n p is the total number of moles of combustion products in the gas phase.

y
n p ¼ n v + z +4:76Λ (8.8)
4 2
The combustion of one mole of fuel with 4.76Λ moles of air yields n p moles

of gaseous products and y n v moles of liquid water. The molar enthalpies
2
and entropies of the air, fuel, and combustion products are determined per
unit mole of the fuel.
1
f p y
a ð Þ + h f ,0
a
0
0
H + H H 0 ¼ Λh O 2 +3:76Λh N 2 0 n v h H 2 O l ðÞ,0
2
_ n f
h i
p
z
y
+ Λ x +
xh CO 2 + n v h H 2 O vðÞ h O 2 +3:76Λh N 2
4 2 0
(8.9)
Recalling that both the air and fuel are supplied to the system at ambient
conditions, Eq. (8.9) can be simplified to
1 h i
f p y y z
a ¼ h f ,0 xh CO 2 ,0 + x +
0
0
H + H H 0 h H 2 O lðÞ,0 h O 2 ,0
2 4 2
_ n f
h i
h H 2 O lðÞ ,0
n v h H 2 O vðÞ,0
(8.10)
Taking the reference temperature and pressure T 0 ¼ 298.15 K and p 0 ¼ 1
bar, the first three terms on the right-hand-side of Eq. (8.10) constitute the
higher heating value (HHV) of the fuel, and the fourth term is zero because
h O 2 ,0 ¼0. The enthalpy difference in the last term is the enthalpy of evap-
oration of water, L . Hence, Eq. (8.10) reduces to
w
0